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Properties

Label 1607.1.b
Level $1607$
Weight $1$
Character orbit 1607.b
Rep. character $\chi_{1607}(1606,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $3$
Sturm bound $134$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1607 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1607.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1607 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(134\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1607, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 13 13 0
Eisenstein series 1 1 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 13 0 0 0

Trace form

\( 13 q - q^{2} - q^{3} + 12 q^{4} - 2 q^{6} - 2 q^{8} + 12 q^{9} + O(q^{10}) \) \( 13 q - q^{2} - q^{3} + 12 q^{4} - 2 q^{6} - 2 q^{8} + 12 q^{9} - 3 q^{12} + 11 q^{16} - q^{17} - 3 q^{18} - q^{23} - 4 q^{24} + 13 q^{25} - 2 q^{27} - q^{31} - 3 q^{32} - 2 q^{34} + 9 q^{36} - q^{37} - q^{41} - 2 q^{46} - 5 q^{48} + 13 q^{49} - q^{50} - 2 q^{51} - q^{53} - 4 q^{54} - q^{59} - 2 q^{62} + 10 q^{64} - q^{67} - 3 q^{68} - 2 q^{69} - 6 q^{72} - q^{73} - 2 q^{74} - q^{75} - q^{79} + 11 q^{81} - 2 q^{82} - q^{89} - 3 q^{92} - 2 q^{93} - 6 q^{96} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1607, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1607.1.b.a 1607.b 1607.b $1$ $0.802$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1607}) \) None 1607.1.b.a \(2\) \(-1\) \(0\) \(0\) \(q+2q^{2}-q^{3}+3q^{4}-2q^{6}+4q^{8}+\cdots\)
1607.1.b.b 1607.b 1607.b $3$ $0.802$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-1607}) \) None 1607.1.b.b \(-3\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+\beta _{1}q^{6}+q^{8}+(1+\beta _{2})q^{9}+\cdots\)
1607.1.b.c 1607.b 1607.b $9$ $0.802$ \(\Q(\zeta_{54})^+\) $D_{27}$ \(\Q(\sqrt{-1607}) \) None 1607.1.b.c \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{1}q^{3}+(1+\beta _{3}-\beta _{6})q^{4}+\cdots\)